# Solve inequality involving modulus

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## Homework Statement

Find the solution set of $\large \frac{|x-1|(x-3)(x-5)^{2010}}{(|x|-3)(|x|+1)} \geq 0$

## Homework Equations

I am required to solve this using Wavy-Curve method

## The Attempt at a Solution

The critical points are 3 and 5. But I don't know what to do with expressions involving modulus signs.

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SammyS
Staff Emeritus
Homework Helper
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## Homework Statement

Find the solution set of $\large \frac{|x-1|(x-3)(x-5)^{2010}}{(|x|-3)(|x|+1)} \geq 0$

## Homework Equations

I am required to solve this using Wavy-Curve method

## The Attempt at a Solution

The critical points are 3 and 5. But I don't know what to do with expressions involving modulus signs.
For what values of x is |x|-3 = 0 ?

For what values of x is |x|+1 = 0 ?

haruspex
Homework Helper
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The critical points are 3 and 5. But I don't know what to do with expressions involving modulus signs.
Not sure how you're defining critical points, but interesting things will happen at -3, 1, 3 and 5. I would break it into the five ranges those points generate and consider each separately.
But first, there's a very easy simplification. Think about the (|x|+1) term.

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For what values of x is |x|-3 = 0 ?

For what values of x is |x|+1 = 0 ?